Difference between revisions of "2019 AMC 10A Problems/Problem 10"
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The number of tiles the bug visits is equal to <math>1</math> plus the number of times it crosses a horizontal or vertical line. As it must cross <math>16</math> horizontal lines and <math>9</math> vertical lines, it must be that the bug visits a total of <math>16+9+1 = \boxed{\textbf{(C) }26}</math> squares. | The number of tiles the bug visits is equal to <math>1</math> plus the number of times it crosses a horizontal or vertical line. As it must cross <math>16</math> horizontal lines and <math>9</math> vertical lines, it must be that the bug visits a total of <math>16+9+1 = \boxed{\textbf{(C) }26}</math> squares. | ||
| − | Note: The general formula for this is <math>a+b-\gcd(a,b)</math> | + | Note: The general formula for this is <math>a+b-\gcd(a,b)</math>. |
==Solution 2 (Troll)== | ==Solution 2 (Troll)== | ||
Revision as of 18:40, 10 February 2019
Problem
A rectangular floor that is 
feet wide and 
feet long is tiled with 
one-foot square tiles. A bug walks from one corner to the opposite corner in a straight line. Including the first and the last tile, how many tiles does the bug visit?
Solution
The number of tiles the bug visits is equal to 
plus the number of times it crosses a horizontal or vertical line. As it must cross 
horizontal lines and 
vertical lines, it must be that the bug visits a total of 
squares.
Note: The general formula for this is 
.
Solution 2 (Troll)
Draw it out using grid paper and a ruler. Carefully counting the squares gives us 26.
See Also
| 2019 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
